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Combined Garvey Kelson Relations for Mass Determinations and Machine Learning

I. Bentley, A. Fiorito, M. Gebran, W. S. Porter, A. Aprahamian

TL;DR

This manuscript generates three Garvey Kelson based mass relations that have been optimized with the goal of predicting nuclear masses the most accurately and compares these results with those from theoretical mass models.

Abstract

Simple Garvey Kelson mass relations applied in two regions are often used as an evaluation metric for machine learning based mass models. These relations have also been used in the training of some machine learning based models. Unfortunately, these Garvey Kelson relations do not broadly sum to zero as is sometimes assumed. In this manuscript, we generate three Garvey Kelson based mass relations that have been optimized with the goal of predicting nuclear masses the most accurately. These three relations have each been optimized for specific tasks. One relation has been optimized to predict the masses on the corner of a 5-by-5 grid. One has been optimized to predict the central mass on that grid, and the last has been optimized to work over the entire grid. Using these relations with the AME 2020 N & Z > 7 data, the central nucleus can be determined with a 129 keV standard deviation, any of the four corner masses with a 472 keV standard deviation, and the overall measure finds a 35 keV standard deviation for a per difference metric. We have compared these results with those from theoretical mass models and have tested the prediction and extrapolation capabilities of the relation that predicts corner masses. We also discuss how these relations can be implemented in machine learning based approaches.

Combined Garvey Kelson Relations for Mass Determinations and Machine Learning

TL;DR

This manuscript generates three Garvey Kelson based mass relations that have been optimized with the goal of predicting nuclear masses the most accurately and compares these results with those from theoretical mass models.

Abstract

Simple Garvey Kelson mass relations applied in two regions are often used as an evaluation metric for machine learning based mass models. These relations have also been used in the training of some machine learning based models. Unfortunately, these Garvey Kelson relations do not broadly sum to zero as is sometimes assumed. In this manuscript, we generate three Garvey Kelson based mass relations that have been optimized with the goal of predicting nuclear masses the most accurately. These three relations have each been optimized for specific tasks. One relation has been optimized to predict the masses on the corner of a 5-by-5 grid. One has been optimized to predict the central mass on that grid, and the last has been optimized to work over the entire grid. Using these relations with the AME 2020 N & Z > 7 data, the central nucleus can be determined with a 129 keV standard deviation, any of the four corner masses with a 472 keV standard deviation, and the overall measure finds a 35 keV standard deviation for a per difference metric. We have compared these results with those from theoretical mass models and have tested the prediction and extrapolation capabilities of the relation that predicts corner masses. We also discuss how these relations can be implemented in machine learning based approaches.
Paper Structure (14 sections, 9 equations, 4 figures, 5 tables)

This paper contains 14 sections, 9 equations, 4 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Experimental Masses and Evaluation Metrics
  3. Mass Difference Relations
  4. Garvey Kelson Relations
  5. Garvey Kelson Relations on a 5-by-5 grid
  6. Other Mass Relations
  7. Methodology
  8. Combined Garvey Kelson Relations
  9. Results
  10. Testing mass models using the new mass relations
  11. Predicting newly measured masses
  12. Extrapolations based on the corners
  13. Discussion for implementation in machine learning based mass models
  14. Summary and Conclusion

Figures (4)

  • Figure 1: The Garvey Kelson mass relationships for experimental values from AME 2020 Wang_2021 a) for two regions. A zoomed-in view of the b) two region GK relationships, and c) three region GK relationships in the region around $N=Z$.
  • Figure 2: The GK mass model difference configurations displayed as matrices for a) group A (transverse), b) group B (longitudinal).
  • Figure 3: The mass model difference configurations displayed as matrices. a) Eqn. (\ref{['eqn:12GK']}) from Ref. GK20, b) Eqn. (\ref{['eqn:GKPD']}), c) Eqn. (\ref{['eqn:GKMiddle']}), and d) Eqn. (\ref{['eqn:GKC']}).
  • Figure 4: Mass model extrapolation comparison for neutron-rich (a) krypton ($Z = 36$), (b) tin ($Z = 50$), and (c) hafnium ($Z = 72$) isotopes. Experimental values from AME 2020 Wang_2021 are included as black circles. Solid lines indicate the existing mass models from Refs. PhysRevC.52.R23PhysRevC.93.034337MOLLER20161WANG2014215PRC112FurtherExploration. The brown dashed line shows the mass prediction using an iterative procedure involving solving for the corner mass based on Eqn. (\ref{['eqn:GKC']}).